Combining the binomial theorem with probabilty

Topics: probability, binomial probability

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Using our counting techniques to solve probability problems.

Topic: probability

Using the counting techniques to solve probability problems

Topic: probability

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Gaussian Random Process

Topic: probability

London School of Hygiene & Tropical Medicine Library & Archives Service

Topic: Probability

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Oct 6, 2015
10/15

by
Tovey, Craig A.

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Title from cover

Topic: PROBABILITY.

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Using the counting techniques of pemutations and combinations to solve probability problems

Topic: probability

Using tree diagrams to list the sample space.

Topic: probability

Putting the different ideas together in order to solve probability problems

Topic: probability

Title from cover

Topic: PROBABILITY.

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Probability paradox

Topic: Probability

Introducing the terms and basic ideas of probabiolity

Topic: probability

This course focuses on Modeling, quantification, and analysis of uncertainty by teaching random variables, simple random processes and their probability distributions, Markov processes, limit theorems, elements of statistical inference, and decision making under uncertainty. This course extends the discrete probability learned in the discrete math class. It focuses on actual applications, and places little emphasis on proofs. A problem set based on identifying tumors using MRI (Magnetic...

Topic: probability

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Notes for probability and statistics

Topic: Probability

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Aug 6, 2016
08/16

by
smee kamchann

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មេរៀនប្រូបាប៊ីលីតេសម្រាប់សិស្សវិទ្យាស្ថានបច្ចេកវិទ្យាកម្ពុជា ឆ្នាំទី២

Topic: Probability

An introduction to probability and some basic theory.

Topic: probability

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Mathematics

Topic: Probability

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probability for engineers

Topic: probability

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Probability-Project dumped with WikiTeam tools.

Topics: wiki, wikiteam, wikispaces, Probability-Project, probability-project,...

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Nov 18, 2015
11/15

by
Florentin Smarandache

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In this paper one generalizes the classical probability and imprecise probability to the notion of “neutrosophic probability” in order to be able to model Heisenberg’s Uncertainty Principle of a particle’s behavior, Schrödinger’s Cat Theory, and the state of bosons which do not obey Pauli’s Exclusion Principle (in quantum physics). Neutrosophic probability is close related to neutrosophic logic and neutrosophic set, and etymologically derived from “neutrosophy”.

Topics: imprecise probability, neutrosophic probability, neutrosophic logic

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In this paper we introduce a new type of classical set called the neutrosophic classical set. After given the fundamental definitions of neutrosophic classical set operations, we obtain several properties, and discussed the relationship between neutrosophic classical sets and others. Finally, we generalize the classical probability to the notion of neutrosophic probability. This kind of probability is necessary because it provides a better representation than classical probability to uncertain...

Topics: Neutrosophic Probability, Neutrosophic Set, Probability Theory

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Nov 14, 2013
11/13

by
Erik Demaine

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Topics: Maths, Statistics and Probability, Probability, Mathematics

Source: http://www.flooved.com/reader/1568

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57

Nov 18, 2015
11/15

by
F. Smarandache

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In this paper one generalizes the classical probability and imprecise probability to the notion of “neutrosophic probability” in order to be able to model Heisenberg’s Uncertainty Principle of a particle’s behavior, Schrödinger’s Cat Theory, and the state of bosons which do not obey Pauli’s Exclusion Principle (in quantum physics). Neutrosophic probability is close related to neutrosophic logic and neutrosophic set, and etymologically derived from “neutrosophy”.

Topics: imprecise probability, neutrosophic probability, neutrosophic logic

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380

Nov 14, 2013
11/13

by
Charles E. Leiserson

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Abstract: This tutorial teaches dynamic multithreaded algorithms using a Cilk-like [11, 8, 10] model. The material was taught in the MIT undergraduate class 6.046 Introduction to Algorithms as two 80-minute lectures. The style of the lecture notes follows that of the textbook by Cormen, Leiserson, Rivest, and Stein [7], but the pseudocode from that textbook has been �Cilki�ed� to allow it to describe multithreaded algorithms. The �rst lecture teaches the basics behind multithreading,...

Topics: Maths, Statistics and Probability, Probability, Mathematics

Source: http://www.flooved.com/reader/1567

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Apr 22, 2014
04/14

by
shaunteaches

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A collection of worked examples and statistics and probability

Topics: ccss, statistics and probability, probability, statistics

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Jun 30, 2018
06/18

by
Romain Couillet

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A class of robust estimators of scatter applied to information-plus-impulsive noise samples is studied, where the sample information matrix is assumed of low rank; this generalizes the study of (Couillet et al., 2013b) to spiked random matrix models. It is precisely shown that, as opposed to sample covariance matrices which may have asymptotically unbounded (eigen-)spectrum due to the sample impulsiveness, the robust estimator of scatter has bounded spectrum and may contain isolated eigenvalues...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1404.7685

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Jun 28, 2018
06/18

by
Fernando Cordero

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We study the common ancestor type distribution in a $2$-type Moran model with population size $N$, mutation and selection, and in the deterministic limit regime arising in the former when $N$ tends to infinity, without any rescaling of parameters or time. In the finite case, we express the common ancestor type distribution as a weighted sum of combinatorial terms, and we show that the latter converges to an explicit function. Next, we recover the previous results through pruning of the...

Topics: Mathematics, Probability

Source: http://arxiv.org/abs/1508.06113

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Jun 28, 2018
06/18

by
Walid Hachem; Adrien Hardy; Jamal Najim

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We study the eigenvalue behaviour of large complex correlated Wishart matrices near an interior point of the limiting spectrum where the density vanishes (cusp point), and refine the existing results at the hard edge as well. More precisely, under mild assumptions for the population covariance matrix, we show that the limiting density vanishes at generic cusp points like a cube root, and that the local eigenvalue behaviour is described by means of the Pearcey kernel if an extra decay assumption...

Topics: Mathematics, Probability

Source: http://arxiv.org/abs/1507.06013

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1.0

Jun 26, 2018
06/18

by
Shen Lin

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We study the typical behavior of the harmonic measure of balls in large critical Galton-Watson trees whose offspring distribution has finite variance. The harmonic measure considered here refers to the hitting distribution of height $n$ by simple random walk on a critical Galton-Watson tree conditioned to have height greater than $n$. We prove that, with high probability, the mass of the harmonic measure carried by a random vertex uniformly chosen from height $n$ is approximately equal to...

Topics: Mathematics, Probability

Source: http://arxiv.org/abs/1502.05584

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Jun 27, 2018
06/18

by
Gregory F. Lawler; Mohammad A. Rezaei

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The Green's function for the chordal Schramm-Loewner evolution $SLE_\kappa$ for $0 < \kappa < 8$, gives the normalized probability of getting near points. We give up-to-constant bounds for the two-point Green's function.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1503.06689

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Jun 27, 2018
06/18

by
Lina Wedrich

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Let $X=\{X(t):t\geq0\}$ be an operator semistable L\'evy process in $\mathbb{R}^d$ with exponent $E$, where $E$ is an invertible linear operator on $\mathbb{R}^d$. For an arbitrary Borel set $B\subseteq\mathbb{R}_+$ we interpret the graph $Gr_X(B)=\{(t,X(t)):t\in B\}$ as a semi-selfsimilar process on $\mathbb{R}^{d+1}$, whose distribution is not full, and calculate the Hausdorff dimension of $Gr_X(B)$ in terms of the real parts of the eigenvalues of the exponent $E$ and the Hausdorff dimension...

Topics: Mathematics, Probability

Source: http://arxiv.org/abs/1506.00615

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Jun 28, 2018
06/18

by
Joaquin Fontbona; Hélène Guérin; Florent Malrieu

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We study the long-time behavior of variants of the telegraph process with position-dependent jump-rates, which result in a monotone gradient-like drift toward the origin. We compute their invariant laws and obtain, via probabilistic couplings arguments, some quantitative estimates of the total variation distance to equilibrium. Our techniques extend ideas previously developed for a simplified piecewise deterministic Markov model of bacterial chemotaxis.

Topics: Mathematics, Probability

Source: http://arxiv.org/abs/1507.03503

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Jun 26, 2018
06/18

by
Giulia Di Nunno; Josep Vives

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In this paper we develop a Malliavin-Skorohod type calculus for additive processes in the $L^0$ and $L^1$ settings, extending the probabilistic interpretation of the Malliavin-Skorohod operators to this context. We prove calculus rules and obtain a generalization of the Clark-Hausmann-Ocone formula for random variables in $L^1$. Our theory is then applied to extend the stochastic integration with respect to volatility modulated L\'evy-driven Volterra processes recently introduced in the...

Topics: Mathematics, Probability

Source: http://arxiv.org/abs/1502.05631

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1.0

Jun 27, 2018
06/18

by
Jérôme Dedecker; Florence Merlevède

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We study the Wasserstein distance of order 1 between the empirical distribution and the marginal distribution of stationary $\alpha$-dependent sequences. We prove some moments inequalities of order p for any p $\ge$ 1, and we give some conditions under which the central limit theorem holds. We apply our results to unbounded functions of expanding maps of the interval with a neutral fixed point at zero. The moment inequalities for the Wasserstein distance are similar to the well known von...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1503.00113

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1.0

Jun 28, 2018
06/18

by
Maria Deijfen; Olle Häggström

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This paper provides a survey of known results and open problems for the two-type Richardson model, which is a stochastic model for competition on $\mathbb{Z}^d$. In its simplest formulation, the Richardson model describes the evolution of a single infectious entity on $\mathbb{Z}^d$, but more recently the dynamics have been extended to comprise two competing growing entities. For this version of the model, the main question is whether there is a positive probability for both entities to...

Topics: Mathematics, Probability

Source: http://arxiv.org/abs/1509.07006

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Jun 28, 2018
06/18

by
Patricia Alonso Ruiz; Alexander S. Rakitko

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We obtain the analogue of the classical result by Erd\"os and Kac on the limiting distribution of the maximum of partial sums for exchangeable random variables with zero mean and variance one. We show that, if the conditions of the central limit theorem of Blum et al. hold, the limit coincides with the classical one. Under more general assumptions, the probability of the random variables having conditional negative drift appears in the limiting distribution.

Topics: Mathematics, Probability

Source: http://arxiv.org/abs/1506.09183

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Jun 30, 2018
06/18

by
Florent Benaych-Georges

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We consider an $n$ by $n$ matrix of the form $A=UTV$, with $U, V$ some independent Haar-distributed unitary matrices and $T$ a deterministic matrix. We prove that for $k\sim n^{1/6}$ and $b^2:=\frac{1}{n}\operatorname{Tr}(|T|^2)$, as $n$ tends to infinity, we have $$\mathbb{E} \operatorname{Tr} (A^{k}(A^{k})^*) \ \lesssim \ b^{2k}\qquad \textrm{and} \qquad\mathbb{E}[|\operatorname{Tr} (A^{k})|^2] \ \lesssim \ b^{2k}.$$ This gives a simple proof (with slightly weakened hypothesis) of the...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1409.3864

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Jun 28, 2018
06/18

by
Maria Deijfen; Willemien Kets

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A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in which each vertex is given a random weight, and vertices with larger weights are more likely to be assigned large subsets. The distribution of the degree of a given vertex is characterized and is shown to depend on the weight of the vertex. In particular, if...

Topics: Mathematics, Probability

Source: http://arxiv.org/abs/1509.07019

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Jun 30, 2018
06/18

by
Feng-Yu Wang

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By using the invariant probability probability measure of a reference SDE/SPDE, integrability conditions on the path-dependent drift are presented for degenerate SDEs/SPDEs to possess weak existence and uniqueness of solutions, as well as the existence, uniqueness and entropy estimates of invariant probability measures. When the reference process satisfies the log-Sobolev inequality, Sobolev estimates are derived for the density of invariant probability measures. The main results are applied to...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1701.01248

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Jun 30, 2018
06/18

by
Sandro Gallo; Nancy L. Garcia; Valdivino Vargas Junior; Pablo M. Rodríguez

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We study two rumor processes on $\N$, the dynamics of which are related to an SI epidemic model with long range transmission. Both models start with one spreader at site $0$ and ignorants at all the other sites of $\N$, but differ by the transmission mechanism. In one model, the spreaders transmit the information within a random distance on their right, and in the other the ignorants take the information from a spreader within a random distance on their left. We obtain the probability of...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1401.0841

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Jun 29, 2018
06/18

by
Omer Angel; Remco van der Hofstad; Cecilia Holmgren

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We consider self-loops and multiple edges in the configuration model as the size of the graph tends to infinity. The interest in these random variables is due to the fact that the configuration model, conditioned on being simple, is a uniform random graph with prescribed degrees. Simplicity corresponds to the absence of self-loops and multiple edges. We show that the number of self-loops and multiple edges converges in distribution to two independent Poisson random variables when the second...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1603.07172

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Jun 29, 2018
06/18

by
Steven N. Evans; Alexandru Hening

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Suppose that $(X_t)_{t \ge 0}$ is a one-dimensional Brownian motion with negative drift $-\mu$. It is possible to make sense of conditioning this process to be in the state $0$ at an independent exponential random time and if we kill the conditioned process at the exponential time the resulting process is Markov. If we let the rate parameter of the random time go to $0$, then the limit of the killed Markov process evolves like $X$ conditioned to hit $0$, after which time it behaves as $X$...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1607.03545

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Jun 29, 2018
06/18

by
Dragana Jankov Maširević; Tibor K. Pogány

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Considering the recently studied Gamma exponentiated exponential Weibull ${\rm GEEW}(\theta)$ probability distribution \cite{PoganySaboor} surprising infinite summations are obtained for series which building blocks are special functions like lower and upper incomplete Gamma, Fox--Wright Psi, Meijer $G$ or Whittaker $W$ functions.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1605.06818

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Jun 29, 2018
06/18

by
Neofytos Rodosthenous; Mihail Zervos

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We consider a new family of derivatives whose payoffs become strictly positive when the price of their underlying asset falls relative to its historical maximum. We derive the solution to the discretionary stopping problems arising in the context of pricing their perpetual American versions by means of an explicit construction of their value functions. In particular, we fully characterise the free-boundary functions that provide the optimal stopping times of these genuinely two-dimensional...

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1609.07419

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Jun 29, 2018
06/18

by
Mustazee Rahman; Balint Virag

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We prove that the random empirical measure of appropriately rescaled particle trajectories of the interchange process on path graphs converges weakly to the deterministic measure of stationary Brownian motion on the unit interval. This is a law of large numbers type result for particle trajectories of the interchange process. After the completion of this manuscript we learned about a result of Durrett and Neuhauser that implies this result.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1609.07745

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Jun 29, 2018
06/18

by
Fabrice Gamboa; Jan Nagel; Alain Rouault

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In these notes we fill a gap in a proof in Section 4 of Gamboa, Nagel, Rouault [Sum rules via large deviations, J. Funct. Anal. 270 (2016), 509-559]. We prove a general theorem which combines a LDP with a convex rate function and a LDP with a non-convex one. This result will be used to prove LDPs for spectral matrix measures and for spectral measures on the unit circle.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1610.02071

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Jun 29, 2018
06/18

by
Daniel Pellegrino; Djair Santos; Joedson Santos

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We provide, among other results, the optimal blow up rate of the constants of a family of Khinchin inequalities for multiple sums.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1610.02178